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hilb

Hilbert matrix

Syntax

H = hilb(n)

Description

H = hilb(n) returns the Hilbert matrix of order n.

Definitions

The Hilbert matrix is a notable example of a poorly conditioned matrix [1]. The elements of the Hilbert matrices are H(i,j) = 1/(i + j – 1).

Examples

collapse all

Compute the fourth-order Hilbert matrix and its condition number to see that it is poorly conditioned.

H = hilb(4)
H =

    1.0000    0.5000    0.3333    0.2500
    0.5000    0.3333    0.2500    0.2000
    0.3333    0.2500    0.2000    0.1667
    0.2500    0.2000    0.1667    0.1429

cond(H)
ans =

   1.5514e+04

References

[1] Forsythe, G. E. and C. B. Moler, Computer Solution of Linear Algebraic Systems, Prentice-Hall, 1967, Chapter 19.

See Also

Introduced before R2006a

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